The methods here seem to hold great promise for the general case, genus \(g \ge 4\) . But there are many difficulties: Presented with a pair of weakly reducing disks \(a \subset A, b \subset B\) , the methods of Casson-Gordon ([1]}) describe how to proceed to exhibit a complete non-separating weakly reducing collection of disks \(a_1, ..., a_{g_1}, b_{g_1 + 1}, ..., b_g\)  for \(T\) . But many choices are involved in creating such a collection, and it is not clear that different choices will lead, via Theorem REF , to the same Powell equivalence class of homeomorophisms to \(T_g\) , even under strong inductive assumptions.
